Investigations on vortices generated at the bilge

INVESTIGATIONS ON VORTICES G E N E R A T E D A T T H E B I L G E

by T . TAGORI (Univ. of Tokyo)

1. INTRODUCTION

A t present, hull forms of huge oil tankers and bulk carriers have become fuller and taken smaller length breadth ratio, and their form factors of frictional resist-ance have become larger generally. By the use of bulbous bow, it has been experienced that the form fac-tor reduced and the streamline was improved at bow'--'. It was considered that vortices generated at the bilge of the entrance and run had some connection with this problem.

I n 1 9 5 2 , Inui and Takezawa observed the flow around the two-dimensional model by means of chemical f\lm^\ From this experimental result, it was i m -agined that vortices existed at the bottom of the en-trance and they were similar to vortices at the leading edge of delta wing'-"'' Okada measured the velocity and direction of flow at the stern'*' in 1 9 5 9 . The existence of a set of vortices at the stern'' was made clear from this result.

The author carried out various experiments, mainly flow observations, in order to study the characteristics of these vortices.

2 . E X P E R I M E N T A L T E C H N I Q U E

I t has been recognized recently that the flow visuali-zation is the important experimental technique in ship-hydrodynamics. Especially, the observation of flow is necessary for the investigation of vortices.

Almost past observations of flow around ship models were carried out near the surface of models only. How-ever, it was required that the flow was observed from the surface of model to a distance place, to investigate vortices, so the tuft grid method was used for this pur-pose. The technique of flow observation by means of

tuft grid is shown in Fig. 1.

The flow near the surface of the model was observed by twin tufts that were fitted on the model. The twin tufts is shown in Fig. 2 .

These observations were made with the naked eye and by photographing and taking moving pictures. As the flow near vortices fluctuated momentarily, the author took a large number of photographs in each experiment.

The velocity of flow around the model was measured by smaH total head tubes and static head tubes.

Above-mentioned experiments were carried out at

Bool

Mirror

Fig. I . Flow observation by means of luft grid

While Tuft _{SSiiaped Ring,}

Model Surface

O Shopad Rin

Soldered fo Pin

Fig. 2. Twin tufts

the circulating water channel, that was convenient to these purpose.

3. E X P E R I M E N T S W I T H A T V / O - D I M E N S I O N A L M O D E L

In the first place, the experiment was carried out with a two-dimensional model ( M . N o . W M - 4 ) . This model had a parabolic water hne, wafl side, knuckled bilge and flat bottom. Principal dimensions of M . N o . W M - 4 are shown in Table 1 . Results of the flow observation by tuft grid method are shown in Fig. 3. A t the forebody, it is found that the down flow along the wall side sepa-rates at the bilge, and a set of conical vortices is gener-ated at the fore bottom. This set of vortices is simflar to the leading edge vortex of delta wing. These vortices have the maximum value of circulation at midship, and at downstream diminish, moving to wafl side and near the water surface. A t the aftbody, the flow runs out from the bottom and separates at the bilge, and a new set of large conical vortices is produced at the side of model. The view of the flow around the M . N o . W M - 4 is shown in Fig. 4 .

4 . E X P E R I M E N T S W I T H T A N K E R M O D E L S Regarding to huge ofl tankers with normal bow

'',1 , / ' ' Model ' If V ' w 1 1 'l / / / / ' , y ^ I-/I'I, _' ••I i ' / ^ ' Bow Vortex Q ,> V ^ » V ^ 1 N ^ » \ % \ S N \ N. N V < \ V V V. V •> ^ S . « 1 1 , 1 -i- i f 1 ' I 1 i S.S.No.7 ^ Model Bow Vortex

':/

m

Fig. 3. Results of flow observation with two-dimensional model WM-4 by means of tuft grid, F„=0.25

experiment are shown in Fig. 5. The flow fluctuates momentarily, but it is found clearly that the direction of flow at the surface of model is different from that at a distant place from the surface. Generally, in fuH load condition the difference of flow direction has a tendency to become larger than baflast condition. The model M G T - 1 B-13 has a small fillet at the connecting part of the bulb with main hiül, large value of curvature at the bilge of the entrance, and minor effect to get fair stream-line. The model MGT-1 B-14 has the large fiUet, small curvature at the bilge, and the smooth flow at the bot-tom of the entrance in each condition. From these re-sults, regarding the hufl having the bulbous bow, it is considered that the design of forms of main hull and fillet is yet a important problem to improve the stream-line at the forebody.

Fig. 4. Flow around two-dimensional model WM-4 (Looking askance upward)

(M.No. M G T - 1 ) and various bulbs (M.No. M G T - 1 B-1 ~ 14), the flow at the bottom of the entrance was observed by twin tufts method. Bulbs were formed on the model M G T - 1 by oily clay. Principal dimensions of M G T - 1 are shown in Table 1. Several results of this

Table 1. Principal dimensions of models

Model No. Cond. B m 1A m Tji-m v m ' 5 m ' Cb Remarks

W M - ^ 1.20 1.20 0.24 0.16 0.16 MGT-1 Full load 2.000 2.049 0.332 0.112 0.112 0.0604 0.946 0.81 MGT-1 Ballast 2.000 2.000 0.332 0.080 0,056 0.0340 0.764 0.75 M G T - 2 Full load 2.000 2.000 0.332 0 . I I 2 0.112 Entrance length: 0.113 Lpp M G T - 2 Ballast 2.000 2.000 0.332 0.080 0.056 Run length : 0.202 Lpp A T - 1 Full load 2.000 0.281 0.105 0.105 0.0478 0.832 0.81

Fig. 5. Flow near fore bottom of tanker models, F„ = 0.166, solid line: red tuft, broken line: white tuft

Fig. 6. Flow at the downstream 0.1 Lpp from AP of M G T - I , Fn=0.166

The flow at each square station on the model M G T - 1 was observed by means of tuft grid. However, at the bottom of the entrance, any vortices were not found out. For this reason, it is considered that vortices are thin, and the tuft grid may effect to alter the flow. A t the stern, a set of vortices is observed clearly. Results of the flow observation and the measurement of stream ve-locity are shown in Fig. 6. The energy of this stern vortices set was calculated from these results. The coef-ficient of the eddy making resistance Cyoa obtained by this calculation is shown in Table 2. Moreover, the result of resistance test is shown in Table 2, in the form

Table 2. Resistance coefficients of M G T - 1

Condition Fn Cvon CT K

Full load 0.166 0.46x 10-3 5.73x10 3 0.34 Ballast 0.166 O.STxlO-' 5.50x10"' 0.27

Resistance coefficients are based on S.

factor K.

5. E X P E R I M E N T S W I T H A N A R K

Same experiments were carried out with an ark model (M.No. M G T - 2 ) as M G T - 1 . The model M G T - 2 had knuckled bilge and a hexagonal waterlme, angle of entrance and run of which were equal to average values of M G T - 1 . Principal dimensions of M G T - 2 are shown in Table 1.

Results of the flow observation and the measurement of stream velocity are shown in Fig. 7. The circulation of bow vortices at the end of the entrance obtained f r o m these results is shown in Table 3. Using the measured angle of inflow to the bottom of the entrance, the circu-lation of vortices at the leading edge of delta wing had same apex angle as MGT-2, obtained by Brown and Michael's method'*', and the circulation of bow vortices on the model MGT-2 calculated by the extended meth-od are shown in Table 3.

Table 3. Circulation of bow vortices on MGT-2

Condition Measured Calculated ( F „ = 0 . ! 6 6 ) Condition (F„=0.166) Delta Wing (Section: —) M G T - 2 (Section: Ll) Full load 0.0429mVs 0.472mVs 0.0566mVs Ballast 0.0425mVs 0.382mVs 0.0459mVs 6. A N E X P E R I M E N T OF BOUNDARY L A Y E R SUCTION TO REDUCE STERN VORTICES

A n experiment of boundary layer suction with a oil tanker model (M.No. A T - 1 ) was attempted in order to reduce a set of stern vortices produced at the bilge of the run. Principal dimensions of A T - 1 are shown in Table 1. The location of slit is shown in Fig. 8.

The flow was observed by tuft grid, for various flux of suction and slit length. A n example of these results is shown in Fig. 8. By the suction f r o m this slit, a set of stern vortices reduces exceedingly, but other vortices near the water surface at the stern have a tendency to become larger.

In this experiment, as the sht was wide, the large value of the suction flux was required in order to reduce vortices sufficiently. But, using appropriate size and lo-cation of slit, the necessary value of flux will become smaller,

After this, the author will carried out further searches on these vortices. The improvement is re-quired on the technique of flow observation, so the author is preparing for usmg hydrogen bubbles as tracer.

S.S. No. 0 (AP)

Fig. 7. Flow around MGT-2, in f u l l load condition, Fn=0.166

Rudder i \ \ ,1 p I ' 1 1 1 ' 1 1 1.1 I I \ ' , - - / / / • , , . ^ - - - ^ / ; • - ^ I I

Wilhout Suction With Suction

(Flux : 0.001 m V s )

WL

Suction Slit

AP

Fig. 8. Result of flow observation at AP of tanker model with and without suction by tuft grid, in f u l l load condition, F „ = 0 . I 8 9

The flow observation with the model of a huge oil tanker, now, is making at steering and turning. I t is found that the location of stern vortices shifts, the vortex on turning side becomes larger and on opposite side smaUer. Moreover, at the stern, the separation appears near the water surface at opposite side of turning. I t is considered that stern vortices have a connection with this separation.

REFERENCES

1) SATO, S., OKADA, S., SUDO, S. and TAKAGI, M . : Effect of a Bulbous Bow upon the Resistance of Ships with Small Length-Beam Ratio and Large Block Coefficient, J.S.N.A. of Japan, Vol. 118 (1965).

2) TAKAHEI, T . : Bulbous Bow Design for Full Hull Forms, J.S.N.A. of Japan, Vol. 119 (1966).

3) I N U I , T . and TAKEZAWA, S.: Chemical Film Methods A p -plied to Laminar Flow Detection and Stream-Line

Meas-(1957).

4) MrrsuYAsu, A. and HAYASHI, M . : Types of Separation Vortex on Swept Wings, J. Japan Soc. Aero. Eng., Vol. 5 (1957).

5) H A L L , M . G . : A Theory for the Core of a Leading-edge Vortex, J. Fluid Mech., Vol. 11 (1961).

6) OKADA, S.: On the Results of Experiments on Rudders

(1959).

7) WiEGHARDT, VOU K . : MessuHgeu im Strömungsfeld an zwei Hintcr-Schifïsmodellen, Schiflfstechnik, Bd. 4 (1957). 8) BROWN, C . E . and MICHAEL, W . H . : Effect of

Leading-edge Separation on the L i f t of a Delta Wing, J. Aero. Sci., V o l . 2 1 (1954).

A P P L I C A T I O N S O F T H E T H E O R Y O F T H E W A V E - M A K I N G R E S I S T A N C E T O F U L L S H I P F O R M S

by M . BESSHO (Defense Academy)

This is a summary of approaches to the problem of the resistance of recent f u l l shaped ships by making use of the wavemaking resistance theory.

It is understood that Michell-Havelock's theory of the wave-making resistance is valid only for thin ships and not for such f u l l ships but there is a possibility of the successful application to this case too.

1. D I R E C T A P P L I C A T I O N

The calculated wave-making resistance by Michel! integral is very high and sinusoidal compared with the experiment so far as we know in low speed range, it is also true that the theory explains well the wave-making phenomena.

Hence, direct calculations of Michell's integral of some models in the J.S.R.A. systematic series as follows^':

a) Ship lines are represented by 6th order poly-nomials respectively in three parts, fore, middle and aft body.

b) Frame lines are approximated by straight lines as the sectional area does not change.

c) Michcll integrals are evaluated by the asymp-totic expansion.

d) Michell integral is applied in the doublet form as follows:

R,, = ^P^

r

'Vc^^o sec 6, (9)p sec^ 0 dff ( 1 )

F{K,0)= Hix,z)e^'-"'^''"'dxdz ( 2 ) J -dJ -L/2

where p is the water density, g the gravity constant, V the speed, Ko=g/V\ H the half breadth, the ;c-axis forwards positive, the z-axis upwards positive and the origin at midship on the still water surface.

A n example is shown as Fig. 1. The qualitative

0.15

0.10

0.05

F r = V / v ' l . g

Fig. 1. Calculated wave-jnaking resistance

correspondence between the theory and the experiment is very good but the calculated values are three or four times larger and very much sinusoidal than those of the experiment.

The one difficulty of these calculation lies on the curve fitting of the ship lines by polynomials in the x-coordinate and it may be preferable to be fi.tted by trigo-nometric functions with the weight function 1 / 4 ( l — x " ) .

The other difficulty is that the representation of the frame line's small variation like the bulbous bow shape is very complex. This may be solved by the introduc-tion of the influence funcintroduc-tion.

2. I N F L U E N C E F U N C T I O N The formula ( 1 ) is written as the next form